Consider the non-right triangle shown below that has lengths of 1.6, 1.751 and 2.6 cm and interior angle measures of 0.72, α, and β degrees. a) What is the value of α? b) What is the value of β?

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Consider the non-right triangle shown below that has lengths of 1.6, 1.751 and 2.6 cm and interior angle measures of 0.72, α, and β degrees.    a) What is the value of α?  b) What is the value of β?

Forneadil · Accepted Answer

Step 1  Let,  a=1.6cm  b=2.6cm  c=1.751cm  And,  A=α, B=β, C=41.253∘  According to sine law:  sin⁡Aa=sin⁡Bb=sin⁡Cc  Step 2  Thus,  sin⁡α1.6=sin⁡41.253∘  sin⁡α=1.6×sin⁡41.253∘1.751  sin⁡α=0.60252  ∴α=37.051∘  Now, using triangle property  A+B+C=180∘  α+β+41.253=180∘  37.051+β=180∘−41.253∘  β=138.747−37.051  ∴β=101.696∘  Step 3  Therefore,  α=37.051∘  β=101.696∘

Consider the non-right triangle shown below that has lengths of 1.6, 1.751 and 2

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